Related papers: Spatial Covariance Constraints for Gaussian Mixtur…
Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…
In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex…
Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically…
We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to…
Spectral clustering is one of the most popular algorithms to group high dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been…
We study the problem of learning Gaussian Mixture Models (GMMs) and ask: which structural properties govern their sample complexity? Prior work has largely tied this complexity to the minimum pairwise separation between components, but we…
Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the…
We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain…
This paper addresses the problem of finding parametric constraints that ensure the validity of the multivariate Mat{\'e}rn covariance for modeling the spatial correlation structure of coregionalized variables defined in an Euclidean space.…
Recent work on overfitting Bayesian mixtures of distributions offers a powerful framework for clustering multivariate data using a latent Gaussian model which resembles the factor analysis model. The flexibility provided by overfitting…
Mixtures of matrix Gaussian distributions provide a probabilistic framework for clustering continuous matrix-variate data, which are becoming increasingly prevalent in various fields. Despite its widespread adoption and successful…
In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
Modeling the time-varying covariance structures of high-dimensional variables is critical across diverse scientific and industrial applications; however, existing approaches exhibit notable limitations in either modeling flexibility or…
The Gaussian cluster-weighted model (CWM) is a mixture of regression models with random covariates that allows for flexible clustering of a random vector composed of response variables and covariates. In each mixture component, it adopts a…
We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the…
In this paper, we introduce a mixture of skew-t factor analyzers as well as a family of mixture models based thereon. The mixture of skew-t distributions model that we use arises as a limiting case of the mixture of generalized hyperbolic…
We quantify the parameter stability of a spherical Gaussian Mixture Model (sGMM) under small perturbations in distribution space. Namely, we derive the first explicit bound to show that for a mixture of spherical Gaussian $P$ (sGMM) in a…